The developed urban models explain the location considering, among others, a variable of general accessibility, which definition and understanding are divergent and ambiguous. In this way we develop a first stage of investigation that raises a new dimension of accessibility (functional probability), that it is constructed with the population pattern of mobility (how the people move in the city). This dimension was compared with traditional measures of accessibility (distance, time), in its capacity to explain the spatial pattern of residential densities, in the metropolitan area of Santiago (Chile) and Barcelona (Spain). The functional probability (“disposition to travel”), in both cities, shows a statistical similarity in the purposes journey to shop and to study, but a dissimilarity in the journey to work purpose. These results are interesting in the sense that Barcelona and Santiago are structurally different. In this context, we develop a second stage of the investigation, based on the new paradigm of understanding the integration of the mobility (transport) in the social territorial system. The newness of the investigation is the way (quantitative) to characterize and to visualize space-time operation of social systems in the city, understanding them not only by the mobility, but also by the space-time behavior of the stay of people in the different zones of the city, with different purposes. The study applies a trip chain analysis (like the activity-based transportation model) over trip surveys for the metropolitan area of Barcelona (2001, 2006), and for Santiago (1991, 2001). The results are analyzed in a probabilistic dimension (aggregate) in space and time. The first result of this second stage of the investigation is the dynamic density (variation in space and time) of the use of the city and the transport network, for different purposes, for the metropolitan area of Barcelona 2001. The functional probability (mobility and activity) approach can be used as a measure of social equity in the use of time in the city.

Peer Reviewed